Chapter 2 Linear Equations in One Variable Ex 2.2 Solutions
Question - 11 : - Fifteen years from now RaviтАЩs age will be four times his present age. What is RaviтАЩs present age?
Answer - 11 : -
Let the present age of Ravi be x.
Fifteen years later, Ravi age will be x+15 years. According to the question,
x + 15 = 4x
тЗТ 4x тАУ x = 15
тЗТ 3x = 15
тЗТ x = 15/3
тЗТ x = 5
Therefore, Present age of Ravi = 5 years.
Question - 12 : - The ages of Rahul and Haroon are in the ratio 5:7. Four years later the sum of their ages will be 56 years. What are their present ages?
Answer - 12 : -
Let the ages of Rahul and Haroon be 5x and 7x. Four years later,
The ages of Rahul and Haroon will be (5x + 4) and (7x + 4) respectively. According to the question,
(5x + 4) + (7x + 4) = 56
тЗТ 5x + 4 + 7x + 4 = 56
тЗТ 12x + 8 = 56
тЗТ 12x = 56 тАУ 8
тЗТ 12x = 48
тЗТ x = 48/12
тЗТ x = 4
Therefore, Present age of Rahul = 5x = 5├Ч4 = 20
And, present age of Haroon = 7x = 7├Ч4 = 28
Question - 13 : - The number of boys and girls in a class are in the ratio 7:5. The number of boys is 8 more than the number of girls. What is the total class strength?
Answer - 13 : -
Let the number of boys be 7x and girls be 5x.
According to the question,
7x = 5x + 8
тЗТ 7x тАУ 5x = 8
тЗТ 2x = 8
тЗТ x = 8/2
тЗТ x = 4
Therefore, Number of boys = 7├Ч4 = 28
And, Number of girls = 5├Ч4 = 20
Total number of students = 20+28 = 48
Question - 14 : - BaichungтАЩs father is 26 years younger than BaichungтАЩs grandfather and 29 years older than Baichung. The sum of the ages of all the three is 135 years. What is the age of each one of them?
Answer - 14 : -
Let the age of BaichungтАЩs father be x.
Then, the age of BaichungтАЩs grandfather = (x+26)
and, Age of Baichung = (x-29) According to the question,
x + (x+26) + (x-29) = 135
тЗТ 3x + 26 тАУ 29 = 135
тЗТ 3x тАУ 3 = 135
тЗТ 3x = 135 + 3
тЗТ 3x = 138
тЗТ x = 138/3
тЗТ x = 46
Age of BaichungтАЩs father = x = 46
Age of BaichungтАЩs grandfather = (x+26) = 46 + 26 = 72
Age of Baichung = (x-29) = 46 тАУ 29 = 17
Question - 15 : - A rational number is such that when you multiply it by 5/2 and add 2/3 to the product, you get -7/12. What is the number?
Answer - 15 : -
Let the rational be x.
According to the question,
x ├Ч (5/2) + 2/3 = -7/12
тЗТ 5x/2 + 2/3 = -7/12
тЗТ 5x/2 = -7/12 тАУ 2/3
тЗТ 5x/2 = (-7- 8)/12
тЗТ 5x/2 = -15/12
тЗТ 5x/2 = -5/4
тЗТ x = (-5/4) ├Ч (2/5)
тЗТ x = тАУ 10/20
тЗТ x = -┬╜
Therefore, the rational number is -┬╜.
Question - 16 : - Lakshmi is a cashier in a bank. She has currency notes of denominations тВ╣100, тВ╣50 and тВ╣10, respectively. The ratio of the number of these notes is 2:3:5. The total cash with Lakshmi is тВ╣4,00,000. How many notes of each denomination does she have?
Answer - 16 : -
Let the numbers of notes of тВ╣100, тВ╣50 and тВ╣10 be 2x, 3x and 5x respectively.
Value of тВ╣100 = 2x ├Ч 100 = 200x
Value of тВ╣50 = 3x ├Ч 50 = 150x
Value of тВ╣10 = 5x ├Ч 10 = 50x According to the question,
200x + 150x + 50x = 4,00,000
тЗТ 400x = 4,00,000
тЗТ x = 400000/400
тЗТ x = 1000
Numbers of тВ╣100 notes = 2x = 2000
Numbers of тВ╣50 notes = 3x = 3000
Numbers of тВ╣10 notes = 5x = 5000